相关论文: Algebraic Bounds on the Rayleigh-B\'enard attracto…
We construct a determining form for the 2D Rayleigh-B\'enard (RB) system in a strip with solid horizontal boundaries, in the cases of no-slip and stress-free boundary conditions. The determining form is an ODE in a Banach space of…
Anelastic convection at high Rayleigh number in a plane parallel layer with no slip boundaries is considered. Energy and entropy balance equations are derived, and they are used to develop scaling laws for the heat transport and the…
We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical…
We study the Rayleigh-B{\'e}nard convection in a 2-D rectangular domain with no-slip boundary conditions for the velocity. The main mathematical challenge is due to the no-slip boundary conditions, since the separation of variables for the…
Analytic bounds on the projection of the global attractor of 2D incompressible turbulence in the palinstrophy--enstrophy plane [Dascaliuc, Foias, and Jolly 2005, 2010] are observed to vastly overestimate the values obtained from numerical…
The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-B\'enard turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure…
We consider Rayleigh-B\'enard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background…
The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-B\'enard convection. Combinations of no-slip, stress-free and periodic boundary conditions are used on both the sidewalls and the horizontal plates.…
A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-B\'{e}nard cell over a four-decade range of Rayleigh numbers has been undertaken aimed at gaining a better insight into the character of the…
In this paper, we study a boundary control problem associated to the stationary Rayleigh-B\'enard-Marangoni (RBM) system in presence of controls for the velocity and the temperature on parts of the boundary. We analyze the existence,…
We study the influence of thermal boundary conditions on large aspect ratio Rayleigh-B\'enard convection by a joint analysis of experimental and numerical data sets for a Prandl number $\mathrm{Pr = 7}$ and Rayleigh numbers $\mathrm{Ra =…
For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are…
The boundary layer flow in a Rayleigh-B\'enard convection cell of rectangular shape has been visualized in this fluid dynamics video. The experiment has been undertaken in air at a Rayleigh number $Ra=1.3\times 10^{10}$ and a Prandtl number…
Rayleigh-B\'enard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised setup to study thermal convection. Of special interest are the statistics of the turbulent…
Rayleigh-B\'enard convection is numerically simulated in two- and three-dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the…
We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh-B\'enard convection for the Rayleigh number range $10^5 \le Ra \le 10^{11}$ and $Pr=0.7$. Using a Cartesian slab…
The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-B\'enard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-B\'enard…
We study Rayleigh-Benard convection in the high-Rayleigh-number and high-Prandtl-number regime, i.e., we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia…
We obtain an analytical bound on the mean vertical convective heat flux $\langle w T \rangle$ between two parallel boundaries driven by uniform internal heating. We consider two configurations, one with both boundaries held at the same…
We revisit the optimal heat transport problem for Rayleigh-B\'enard convection in which a rigorous upper bound on the Nusselt number, $Nu$, is sought as a function of the Rayleigh number $Ra$. Concentrating on the 2-dimensional problem with…